Reviewer:a e b
April 17, 2012 Subject:
a thin book with content
Poole, Introduction to the theory of Linear Differential Equations, is a combination. The first 5 chapters treat elementary subjects, but they add material not usually seen in standard introductions. Chpater 6, 'The Hypergeometric Equation', begins the more advanced material. Indeed, chapter 6 has a wealth of material. Chapter 7 is related to chapter 6, but chapters 8, 9 and 10 are basically independent, being on specialized topics.
If you use Linear Differential Equations on a regular basis, this book has some interesting tricks that will save you time and effort. But if you want to deal with Ordinary Differential Equations generally, I suggest you try some other book. Two classics that I like are Coddington and Levinson, Theory of Ordinary Differential Equations, 1955, and A. R. Forsyth, Theory of Differential Equations (which is available in Internet Archive).